The relation of \(O_C\)  and \(A_C\)  players is qualitatively different at higher \(r\)  value, which has a significant consequence on the final outcome. This process is shown in the bottom row. Due to the higher \(r\)  value \(O_C\)  players can support each other more effectively and they gradually crowd out \(A_C\)  players. This process is illustrated by a declining island of dark blue \(A_C\)  state and marked by an ellipse in panel (e). But light blue \(O_C\)  cannot be happy too long because they become vulnerable against light red \(O_D\)  players. We should note that the value of \(r\)  is still too small to ensure a stable coexistence between different players with \(``O"\)  attitude. Consequently, the fat light blue \(O_C\)  domain starts shrinking, as it is illustrated by panel (f). Notably, defectors with different attitudes are neutral to each other: in the absence of cooperators there is no one to exploit, hence zero payoff difference in Eq. REF  dictates a random adoption of an attitude between defector players. There is however, a slight asymmetry which gives an advantage to \(O_D\) : when cooperators are still alive then their vicinity offers a higher propagation chance to \(O_D\) . Note that \(A_C\)  or \(O_C\)  would coexist with \(A_D\)  because they should play the traditional prisoner's dilemma game with the latter player. But \(O_D\)  propagates more efficiently in cooperator domains which results in a higher portion of \(O_D\)  when only defectors remain. This stage is shown in panel (g). We stress that, however, this is not the final state because the surface-tension free voter-model like coarsening will result in a homogeneous final destination [1]}. Indeed, this is a logarithmically slow process where the attitude which has larger initial are has a higher chance to prevail [2]}, [3]}.
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